On the dual of (non)-weakly regular bent functions and self-dual bent functions

Ayça Çeşmelioǧlu; Wilfried Meidl; Alexander Pott

doi:10.3934/amc.2013.7.425

Article Contents

2013, Volume 7, Issue 4: 425-440. Doi: 10.3934/amc.2013.7.425

This issue Previous Article The cross-correlation distribution of a $p$-ary $m$-sequence of period $p^{2k}-1$ and its decimated sequence by $\frac{(p^{k}+1)^{2}}{2(p^{e}+1)}$ Next Article Quotients of orders in cyclic algebras and space-time codes

On the dual of (non)-weakly regular bent functions and self-dual bent functions

1.
Faculty of Mathematics, Otto-von-Guericke University, Universitätsplatz 2, 39106, Magdeburg
2.
MDBF, Sabanci University, Orhanlı, Tuzla 34956, İstanbul

Received: July 2012

Revised: March 2013

Published: November 2013

Abstract / Introduction Related Papers Cited by

Abstract

For weakly regular bent functions in odd characteristic the dual function is also bent. We analyse a recently introduced construction of non-weakly regular bent functions and show conditions under which their dual is bent as well. This leads to the definition of the class of dual-bent functions containing the class of weakly regular bent functions as a proper subclass. We analyse self-duality for bent functions in odd characteristic, and characterize quadratic self-dual bent functions. We construct non-weakly regular bent functions with and without a bent dual, and bent functions with a dual bent function of a different algebraic degree.

Keywords:

Mathematics Subject Classification: Primary: 11T71, 94A60, 06E30; Secondary: 11T24.

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